The Extension Spaces of Nonsymmetric Classical Domains
We have introduced some new types of nonsymmetric classical domains in Ref. 4, whose special cases are the examples of Ref. 3. In this chapter we discuss “extension spaces” for these domains. To define “extension space,” we introduce infinite distance points. In one complex variable, the Gauss plane can be compactified by introducing the unique infinite distance point, which is very convenient in many problems. In several complex variables, extension spaces for the four types of classical symmetric domains are well known. But for nonsymmetric domains, there is only Ref. 2.
KeywordsComplex Manifold Motion Group Grassmann Manifold Extension Space Classical Domain
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- 1.Lu Qi-Keng. Classical Manifolds and Classical Domains, Shanghai Science and Technology, Shanghai (1963)Google Scholar
- 2.Lu Qi-Keng. A class of homogeneous complex manifolds, Acta Math, Sinica 12, 229–249 (1962).Google Scholar
- 3.I. I. Pyateckii-Shapiro, Automorphic Functions and the Geometry of Classical Domains, Gordon and Breach, New York (1969)Google Scholar
- 4.Zhong Jia-Qing and Yin Wei-Ping. Some types of nonsymmetric homogeneous domains, Acta Math. Sinica 24, 587–613 (1981) (Chapter 10 of this volume)Google Scholar